Question

(ii) Express the rational number 1/13 in decimal form and hence find the
decimal expansion of 3/13, 4/13 and 5/13.
​

Answer 1

Solution:

We have to express the rational number $\frac{1}{13}$ in decimal form.

$\sf{\underline{Hence:}}$

We have to find the decimal expansion of:

$\frac{3}{13}$, $\frac{4}{13}$ and $\frac{5}{13}$.

$\sf{\underline{In\: order\:to\:get\:the\:answer:}}$

Divide 1 by 13 in order to get 0.(076923) in repeating form.

$\sf{\underline{Now:}}$

$\boxed{\sf{\frac{2}{13} \:can\:be\:written\:as\: 2 \frac{1}{13}}}$

$\sf{\underline{So:}}$

The multiple decimal form of $\frac{1}{13}$ from 2 to get 0.(153846) in repeating form.

$\sf{\underline{And\:now\:we\:get:}}$

$\implies$ $\boxed{\sf{ \frac{3}{13} = 0.(230769)}}$

$\implies$ $\boxed{\sf{ \frac{4}{13} = 0.(307692)}}$

$\implies$ $\boxed{\sf{\frac{5}{13} = 0.(384615)}}$

$\sf{\underline{Final\:answer:}}$

0.(230769), 0.(307692) and 0.(384615).

Answer 2

Answer:

0.2307692

Answer. Decimal form of 3/13 is 0.2307692. Decimal expansion is the Terminating and repeating which is about 9th numbers is repeating it. Converting the fraction to the decimal which is easily dividing numerator by denominator is the correct answer that is 0.2307692.